Question

Is Blocking Design possible for this problem? :)

Answer 1

Is it possible to design a blocking design for this situation:

A study was undertaken to assess the effect of sheer size of a portfolio (leaving out all other effects, such as degree of diversification) on abnormal performance, that is, performance of a stock portfolio that is above what one can expect based on the stock market as a whole. In a four-factor design based on portfolio size for well- diversified portfolios, with 240 data points, the F statistic was significant at the 1% level of significance. Explain

Answer 2

The wording of the problem is a bit unclear. Traditionally, a "four-factor design" means there are four categorical predictors of an outcome (e.g., sex, race, eye color, hair color predicting salary, to use a silly example). This may include interaction terms (with four factors, that gets unwieldy pretty quickly). But the problem also states that the question of interest has to do with portfolio size predicting abnormal performance, "leaving out all other effects."

So I really don't know how to interpret the four-factor language. I could guess and say what the author *really* means is a model where the predictor has four *levels* (small, medium, large, huge) and the outcome is abnormal performance. This would be a much more tractable problem with an interpretable F-statistic. In this case you're looking at a one-way ANOVA (analysis of variance). The null hypothesis is that the expected outcome is the same for the four sizes of portfolio. So how would you interpret a significant F statistic?